Statistical distribution of wave heights attenuation by entrained air bubbles in the surf zone

The paper focuses on the wave height distribution functions for long-term behavior of significant wave height, probability density function, Rayleigh distribution, depth-limited wave height distributions, etc. We have introduced the air bubble effects in the surf zone wave parameters, and the wave height distribution has been derived from the Rayleigh distribution. The calculated statistical wave height distributions by the present model indicate a good agreement with the field data than the Rayleigh distribution. Furthermore, the computed probability densities of the wave heights have been reduced considerably by the air bubble effects, making the wave heights lower than those determined by the Rayleigh distribution. It is also observed that the Rayleigh distribution overestimates large pressure amplitudes, but the present model and the Weibull distribution agree well with the collected field data. Finally, the proposed model performs less normalized root-mean-square error in predicting wave height statistics.